A104145 a(1) = 1; let A(k) = sequence of first 2^(k-1) terms; then A(k+1) is concatenation of A(k) and (A(k)-1) if a(k) is odd, or concatenation of A(k) and (A(k)+1) if a(k) is even.

1, 0, 2, 1, 2, 1, 3, 2, 0, -1, 1, 0, 1, 0, 2, 1, 2, 1, 3, 2, 3, 2, 4, 3, 1, 0, 2, 1, 2, 1, 3, 2, 0, -1, 1, 0, 1, 0, 2, 1, -1, -2, 0, -1, 0, -1, 1, 0, 1, 0, 2, 1, 2, 1, 3, 2, 0, -1, 1, 0, 1, 0, 2, 1, 0, -1, 1, 0, 1, 0, 2, 1, -1, -2, 0, -1, 0, -1, 1, 0, 1, 0, 2, 1, 2, 1, 3, 2, 0, -1, 1, 0, 1, 0, 2, 1, -1, -2, 0, -1, 0, -1, 1, 0, -2, -3, -1, -2, -1, -2, 0, -1, 0, -1, 1

Offset

1,3

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..8192

Formula

a(n) = 1 - A137412(n). - Leroy Quet, Apr 22 2008

Example

a(3) = 2 is even, so A(4) (1,0,2,1,2,1,3,2), the first 8 terms of the sequence, is A(3) (1,0,2,1) concatenated with each term of A(3) plus one (2,1,3,2).

Prog

(Python)
from itertools import count, islice
def a_gen():
    yield 1
    A = [1]
    for k in count(0):
        for i in range(2**(k)):
            x = A[i]+(-1)**abs(A[k])
            A.append(x)
            yield x
A104145_list = list(islice(a_gen(), 100)) # John Tyler Rascoe, Jun 17 2024

Crossrefs

Cf. A137412.

Sequence in context: A134780 A247379 A154819 * A230981 A123675 A356226

Adjacent sequences: A104142 A104143 A104144 * A104146 A104147 A104148

Keyword

easy,sign

Author

Leroy Quet, Mar 07 2005

Extensions

More terms from Joshua Zucker, May 10 2006

Status

approved